This is an announcement for the paper "Noncommutative integral inequalities for convex functions of maximal functions and applications" by Turdebek N. Bekjan and Zeqian Chen.
Abstract: In this paper, we establish a Marcinkiewicz type interpolation theorem for convex functions of maximal functions in the noncommutative setting. As applications, we prove the noncommutative analogue of the Doob inequality for convex functions of maximal functions on martingales, the analogue of the classical Dunford-Schwartz maximal ergodic inequality for convex functions of positive contractions, and that of Stein's maximal inequality for convex functions of symmetric positive contractions. As a consequence, we obtain the moment Burkholder-Davis-Gundy inequality for noncommutative martingales.
Archive classification: math.FA math.PR
Remarks: 18 pages
Submitted from: chenzeqian@hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.2795
or